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Adding two small changes.
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rafalab committed Sep 23, 2024
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2 changes: 1 addition & 1 deletion inference/bayes.qmd
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Expand Up @@ -114,7 +114,7 @@ $$
\frac{0.99 \cdot 0.00025}{0.99 \cdot 0.00025 + 0.01 \cdot (.99975)} = 0.02
$$

According to the above, despite the test having 0.99 accuracy, the probability of having the disease given a positive test is only 0.02. This might seem counter-intuitive to some, but it ss because we must factor in the very rare probability that a randomly chosen person has the disease. To illustrate this, we run a Monte Carlo simulation.
According to the above, despite the test having 0.99 accuracy, the probability of having the disease given a positive test is only 0.02. This might seem counter-intuitive to some, but it is because we must factor in the very rare probability that a randomly chosen person has the disease. To illustrate this, we run a Monte Carlo simulation.

### Bayes theorem simulation

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2 changes: 1 addition & 1 deletion prob/discrete-probability.qmd
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Expand Up @@ -16,7 +16,7 @@ A more tangible way to think about the probability of an event is as the proport

We use the notation $\mbox{Pr}(A)$ to denote the probability of event $A$ occurring. We use the very general term *event* to refer to things that can happen when something occurs by chance. In our previous example, the event was "picking a red bead." In a political poll, where we randomly phone 100 likely voters at random, an example of an event is "calling 48 Democrats and 52 Republicans."

In data science applications, we often encounter continuous variables. These events will often be questions, such as "Is this person taller than 6 feet?" In these cases, we represent events in a more mathematical form: $X \geq 6$. We will see more of these examples later, but for now, we will focus on categorical data.
In data science applications, we often encounter continuous variables. These events will often be questions, such as "Is this person taller than 6 feet?" In these cases, we represent events in a more mathematical form: $X > 6$. We will see more of these examples later, but for now, we will focus on categorical data.

## Probability distributions

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